Multi-dimensional electronic circuitry formed upon bicontinuous structures

ABSTRACT

A three-dimensional circuit includes a hyperbolic bicontinuous structure forming a substrate; circuits formed on a first surface of the hyperbolic bicontinuous structure; and electrically conductive traces formed between the circuits. The electrically conductive traces are formed two-dimensionally on the first surface of the hyperbolic bicontinuous structure. The electrically conductive traces are effectively three-dimensional traces between the circuits.

PRIORITY INFORMATION

This application is a continuation of co-pending U.S. patent applicationSer. No. 13/550,923, filed on Jul. 17, 2012. This application claimspriority, under 35 U.S.C. §120, from co-pending U.S. patent applicationSer. No. 13/550,923, filed on Jul. 7, 2012, said co-pending U.S. patentapplication Ser. No. 13/550,923, filed on Jul. 17, 2012, claimingpriority, under 35 U.S.C. §119(e), from U.S. Provisional PatentApplication, Ser. No. 61/508,660, filed on Jul. 17, 2011; U.S.Provisional Patent Application, Ser. No. 61/547,184, filed on Oct. 14,2011; and U.S. Provisional Patent Application, Ser. No. 61/671,878,filed on Jul. 16, 2012. The entire content of co-pending U.S. patentapplication Ser. No. 13/550,923, filed on Jul. 17, 2012, is herebyincorporated by reference.

This application claims priority, under 35 U.S.C. §119(e), from U.S.Provisional Patent Application, Ser. No. 61/508,660, filed on Jul. 17,2011. The entire content of U.S. Provisional Patent Application, Ser.No. 61/508,660, filed on Jul. 17, 2011, is hereby incorporated byreference.

This application further claims priority, under 35 U.S.C. §119(e), fromU.S. Provisional Patent Application, Ser. No. 61/547,184, filed on Oct.14, 2011. The entire content of U.S. Provisional Patent Application,Ser. No. 61/547,184, filed on Oct. 14, 2011, is hereby incorporated byreference.

BACKGROUND

Light modulating mirror devices have been developed in which a mirror orreflector is can be positioned at various locations to either direct theimpinging light to one location or to direct the impinging light toanother location.

When a voltage is applied to one region housing the mirror, the mirroris moved so that the impinging light is directed to a first location.When the voltage is removed or applied to another region housing themirror, the mirror is moved so that the impinging light is directed to asecond location.

Such a device can be implemented in a variety of optical applications.For example, U.S. Pat. No. 5,061,049, issued on Oct. 29, 1991, entitled“Spatial Light Modulator and Method,” describes a spatial lightmodulator with a movable mirror.

Spatial light modulators are transducers that modulate incident light ina spatial pattern corresponding to an electrical or optical input. Theincident light may be modulated in its phase, intensity, polarization,or direction, and the light modulation may achieved by a variety ofmaterials exhibiting various electrooptic or magnetoopotic effects andby materials that modulate light by surface deformation.

An example of a prior art single pixel electrostatic (rigid) movablemirror device is illustrated by FIG. 1. The pixel, generally denoted 20,is basically a plate (flap) covering a shallow well and includes siliconsubstrate 22, insulating spacer 24, metal hinge layer 26, metal platelayer 28, plate 30 formed in layers 26-28, and plasma etch access holes32 in plate 30. The portions 34 & 36 of hinge layer 26 that are notcovered by plate layer 28 form torsion hinges (torsion rods) attachingbeam 30 to the portion of layers 26-28 supported by spacer 24.Electrodes 40, 42, 46, and 41 run between spacer 24 and substrate 22 andare isolated from substrate 22 by silicon dioxide layer 44.

The design of FIG. 1 allows that the plate metal be as thick as desiredand the hinge metal be as thin as desired without the problems of stepcoverage of the hinge metal over the plate metal and that the spacersurface under the beam metal is not exposed to processing side effectswhich would arise if the hinge were formed as a rectangular piece on thespacer prior to deposition of the plate metal.

Pixel 20 is operated by applying a voltage between metal layers 26-28and electrodes 42 or 46 on substrate 22: beam 30 and the electrodes formthe two plates of an air gap capacitor and the opposite charges inducedon the two plates by the applied voltage exert electrostatic forceattracting beam 30 to substrate 22, whereas electrodes 40 and 41 areheld at the same voltage as beam 30. This attractive force causes beam30 to twist at hinges 34 and 36 and be deflected towards substrate 22.

FIG. 1 also indicates the reflection of light from deflected beam 30 asmay occur during operation of a deformable mirror device. The deflectionof beam 30 can be a highly non-linear function of the applied voltagebecause the restoring force generated by the twisting of hinge 34 isapproximately a linear function of the deflection but the electrostaticforce of attraction increases as a function of the reciprocal of thedistance between the closest corner of beam 30 and substrate 22.

Conventional optical switches provide single path switching for singlelasers or single beam of light.

Therefore, it is desirable to provide an optical switching system thatis capable of multiple sub-pathway switching without negativelyimpacting the switching speed. Furthermore, it is desirable to providean optical switching system that is capable of handling multiple lasersor beams of light without negatively impacting the switching speed.

It is noted that higher integration of semiconductor devices is desiredfor superior performance and/or reducing the price of electronicdevices.

Accordingly, three-dimensional semiconductor devices having a stackedstructure have been fabricated, wherein the stacked structure includes afirst layer, a second layer, a third layer, and a fourth layersequentially stacked on a substrate. An example of such a structure isillustrated in FIG. 29.

In FIG. 29, a first layer 2110 is formed. Upon the first layer 2110,circuits 2205 and 2210 are formed. In this example, circuits 2205 and2210 are formed on the same plane of layer 2110. Wiring or conductivetraces 2310 are formed between circuits 2205 and 2210.

Upon first layer 2110, a second layer 2120 is formed. It is noted thatan air gap may be formed between first layer 2110 and second layer 2120.

Upon the second layer 2120, circuits 2215 and 2220 are formed. In thisexample, circuits 2215 and 2220 are formed on the same plane of layer2120. Wiring or conductive traces 2325 are formed between circuits 2215and 2220.

Upon second layer 2120, a third layer 2130 is formed. It is noted thatan air gap may be formed between second layer 2120 and third layer 2135.

Upon the third layer 2130, circuits 2225, 2230, and 2235 are formed. Inthis example, circuits 2225, 2230, and 2235 are formed on the same planeof layer 2130. Wiring or conductive traces 2340 and 2345 are formedbetween circuits 2225, 2230, and 2235.

Upon third layer 2130, a fourth layer 2140 is formed. It is noted thatan air gap may be formed between third layer 2130 and fourth layer 2140.

Upon the fourth layer 2140, circuits 2240, 2245, and 2250 are formed. Inthis example, circuits 2240, 2245, and 2250 are formed on the same planeof layer 2140. Wiring or conductive traces 2360 and 2365 are formedbetween circuits 2240, 2245, and 2250.

To provide electrical connectivity between layers, wiring or conductivetraces 2425 and 2475 are vertically formed between layers 2110, 2120,2130, and 2140. Wiring or conductive traces 2305, 2315, 2320, 2330,2335, 2350, 2355, and 2370 are formed to provide electrical connectivitybetween the various circuits and vertical conductive traces 2425 and2475.

It is noted that wiring or conductive traces 2425 and 2475 may beintegral with wiring or conductive traces 2305, 2315, 2320, 2330, 2335,2350, 2355, and 2370.

Another example of a stacked structure is disclosed in Published USPatent Application Number 2012/0171861. The entire content of PublishedUS Patent Application Number 2012/0171861 is hereby incorporated byreference.

In these conventional devices, the conductive traces that provideconnectivity between levels or layers include 90 degree bends. These 90degree bends can produce heat, consume power, and radiate noise.

Moreover, it is desirable to provide a three-dimensional circuitarchitecture that realizes less heat, less power consumption, optimallyshorter paths, and higher connectivity options.

Furthermore, it is desirable to have a three dimensional circuit ordevice that is confined to a two dimensional substrate.

BRIEF DESCRIPTION OF THE DRAWINGS

The drawings are only for purposes of illustrating embodiments and arenot to be construed as limiting, wherein:

FIG. 1 illustrates single pixel electrostatic (rigid) movable mirrordevice;

FIG. 2 illustrates a block diagram of an optical switching system usinga bicontinuous structure;

FIG. 3 illustrates an example of a bicontinuous optical switchingstructure directing primary photons originating from a green laser in apredetermined direction;

FIG. 4 illustrates another example of a bicontinuous optical switchingstructure directing primary photons originating from a green laser in apredetermined direction;

FIG. 5 illustrates a third example of a bicontinuous optical switchingstructure directing primary photons originating from a green laser in apredetermined direction;

FIG. 6 illustrates a fourth example of a bicontinuous optical switchingstructure directing primary photons originating from a green laser in apredetermined direction;

FIG. 7 illustrates an example of a bicontinuous optical switchingstructure directing primary photons originating from multiple lasers indifferent predetermined directions;

FIG. 8 illustrates another example of a bicontinuous optical switchingstructure directing primary photons originating from multiple lasers indifferent predetermined directions;

FIG. 9 illustrates a third example of a bicontinuous optical switchingstructure directing primary photons originating from multiple lasers indifferent predetermined directions;

FIG. 10 illustrates a block diagram of an optical switching system usinga bicontinuous structure and embedded electronic devices in or on thehyperbolic internal structures;

FIG. 11 shows an entry angle or trajectory of laser beams entering theopening of a tunnel of a bicontinuous structure from a perspective oflooking into the entrance of the tunnel;

FIG. 12 shows an entry angle or trajectory of laser beams entering theopening of a tunnel of a bicontinuous structure from a perspective oflooking across the face of the entrance of the tunnel;

FIG. 13 shows an example of a device having multiple points withhyperbolic curvature, forming a single bicontinuous structure having anoriented, two-sided surface separating congruent and mutuallyinterpenetrating tunnel labyrinths;

FIG. 14 shows another example of a device having multiple points withhyperbolic curvature, forming a single bicontinuous structure comprisingan oriented, two-sided surface separating congruent and mutuallyinterpenetrating tunnel labyrinths;

FIG. 15 shows a third example of a device having multiple points withhyperbolic curvature, forming a single bicontinuous structure comprisingan oriented, two-sided surface separating congruent and mutuallyinterpenetrating tunnel labyrinths; In this case the structure is randomwith no repeating motifs, whereas in FIGS. 13 and 14 the structures canbe repeated infinitely in 3 dimensions using crystallographic symmetryoperations;

FIG. 16 shows an example of a bicontinuous structure where one of thetwo sets of tunnels has been closed by ellipsoidal caps;

FIG. 17 illustrates a second bicontinuous structure where one of the twosets of tunnels has been closed by ellipsoidal caps;

FIG. 18 illustrates an annotated example of a device having a randombicontinuous structure with mutually interpenetrating labyrinths;

FIGS. 19-21 illustrate networks comprised of nodes and traces (verticesand edges) having a fully three-dimensional structure, with atwo-dimensional wiring architecture that is fully embedded within or onthe surface;

FIG. 22 illustrates the three-dimensional nature of the network;

FIG. 23 shows an example of multiple photonic crystals each comprised ofhyperbolic, triply periodic bicontinuous structures;

FIG. 24 illustrates an example of a bicontinuous, triply periodicminimal surface structure on which a two-dimensional pattern for acircuit and electronic devices has been embedded;

FIG. 25 illustrates an example of one-eighth of a unit cell of the“Batwing’ minimal surface structure;

FIG. 26 illustrates an example of a CLP minimal surface structure;

FIG. 27 illustrates another example of a CLP minimal surface structure;

FIG. 28 illustrates an example of a catenoid minimal surface structure;

FIG. 29 illustrates a conventional three-dimensional circuit;

FIG. 30 illustrates an example of locating circuitry on a hyperbolicbicontinuous structure; and

FIG. 31 illustrates an example of locating circuitry on one side of ahyperbolic bicontinuous structure and having a coolant flow along theother side of the hyperbolic bicontinuous structure.

DETAILED DESCRIPTION

For a general understanding, reference is made to the drawings. In thedrawings, like reference have been used throughout to designateidentical or equivalent elements. It is also noted that the variousdrawings may not have been drawn to scale and that certain regions mayhave been purposely drawn disproportionately so that the features andconcepts could be properly illustrated.

As discussed above, it is desirable to provide an optical switchingsystem that is capable of multiple sub-pathways switching withoutnegatively impacting the switching speed. Furthermore, it is desirableto provide an optical switching system that is capable of handlingmultiple lasers or beams of light without negatively impacting theswitching speed. An example of such an optical switching system isillustrated in FIG. 2.

As illustrated in FIG. 2, a laser source 500 provides a single laserwhose primary photons can be directed in multiple directions, asillustrated by any one of the dashed line arrows 550. The laser 550 isinputted into a bicontinuous optical switching structure 700, at apredetermined point of entry and trajectory.

The primary optical path though the structure 700 is defined by puregeometric optics; i.e., the angle of incidence and angle of reflectionare identical for photons incident on any surface encountered. Theprimary path is defined only for 100% reflective perfectly smoothsurfaces, and is not subject to deviations due to scattering diffractionand other optical phenomena.

Primary photons are defined as photons that travel on the primary path.The primary optical exit is the exit that primary photons take afterfollowing the primary optical path.

Secondary photons are defined as those photons that travel on pathsother than the primary path and exit at points and angles different fromthat of the primary photons. Photons from the laser travel through thebicontinuous optical switching structure 700. Photons from the laser 600exits a primary exit point depending upon the predetermined point ofentry and/or angle. The exiting primary or secondary photons can becollected by a device or devices 800 for sensing, illumination, heating,further transmission, processing, and/or modulation, etc.

The bicontinuous optical switching structure 700 is an optical switchingsystem that includes a large number of switching channels. The switchingchannels are all optical and do not impede signal transmission.

As noted above, the optical switch comprises complex bicontinuousstructures formed of bicontinuous surfaces. Examples of bicontinuoussurfaces are bicontinuous minimal surfaces, such as the gyroid (the Dand the P surfaces). Such bicontinuous surfaces are well known to thoseskilled in the art.

The bicontinuous structures are characterized by mutuallyinterpenetrating labyrinths and contain a hyperbolically curvedinterface.

It is noted that the term hyperbolic refers only to the curvature at apoint. The average curvature of the surface extended to infinity couldindicate that the overall average surface curvature is hyperbolic.

It is noted that there may be some flat points and points of positiveGaussian curvature in the structures, but on average each point has ahyperbolic curvature; i.e., the two principle curvatures at a point areof opposite signs, and thus, the product thereof or Gaussian curvatureis negative.

The bicontinuous optical switching structure 700 includes apredetermined arrangement tunnels which can be coated with a reflectivematerial or ground or polished to a very smooth surface to provide thedesired reflective properties.

The tunnels can provide pathways from points on the exterior boundingsurface of the bicontinuous structure via one or a series of reflectionsthrough the three-dimensional bicontinuous optical switching structure700 to a second set of points at another location on the exterior of thebicontinuous structure. It is noted that both of the tunnel labyrinthsare continuous from one side of the bicontinuous structure to the otherbecause of the multiple branched connections each tunnel has. The tunnelbranching provides a greater number of the multiple exit points in athree-dimensional space than if the tunnels did not contain branchpoints.

Each open tunnel entrance on the exterior of a bicontinuous structurecontains a plurality of potential optical entry points. Each potentialoptical entry point may be a physical location on one or the other sideof the bicontinuous structure.

The distribution of curvature in the structure can vary. In the mosthomogeneous case, the surface is called the gyroid. Other known surfaceshave more curvature variation. The mean curvature at each point can beconstant or close to constant. These are the set of mean curvaturesurfaces.

It is further noted that, with respect to a bicontinuous surface, alight beam enters one set of branched tunnels at a point and exits fromthe same set of branched tunnels. Thus, there are in fact two sets ofpossible inputs and outputs, unless punctures are placed in the surfaceto allow photons to travel to the other side. A single puncture meansthe surface no longer defines a set of separate tunnel labyrinths sincethe tunnels are now connected. Thus, the system is no longer formallybicontinuous.

In addition to bicontinuous surfaces, the optical switch may be formedof tricontinuous surfaces and multi-continuous surfaces in whichmultiple sets of tunnel systems are separated by a single surface. Inthese cases, there will be multiple sets of unconnected branching tunnelnetworks within the structure. These can also be of high and lowsymmetry, high and low degree of periodic order and with and withoutpunctures.

It is noted that the optical switch may be formed of nested sets ofbicontinuous surfaces.

In addition, it is noted that the optical switch may be formed ofbicontinuous or multi-continuous surfaces, and variations thereof, incombination with any other surface either on the inside or outside ofthe structure. For example, a bicontinuous surface may be utilized witha sphere in a tunnel.

In addition, each potential optical entry point for a tunnel maycorrespond to a different angle of incidence at a single physicallocation on the bicontinuous structure.

Furthermore, each potential optical entry point may be a physicallocation on the bicontinuous structure and each potential optical entrypoint may correspond to a different angle of incidence at the physicallocation on the bicontinuous structure such that the multiple potentialoptical entry points form a three-dimensional set of potential opticalentry points for each tunnel.

Depending upon the entry point and the entry angle, photons from theentering light beam will exit as primary photons at a precise point fromthe bicontinuous optical switching structure 700 defined by the primaryoptical path. In other words, the angle of entry and the entry point(assuming multiple entry points) dictates the position and angle of theexiting light beam or photons at the primary exit point.

It is further noted that each entry point may have several output pointsif, for example, the photon splits in two or for any other reason thatcauses the path to deviate from the geometrically defined primary path.These are defined as secondary photons. Secondary photons are defined asthose that travel along paths other than the primary path and exit frompoints other than primary exit points and in directions other than theprimary trajectories (angles) along from the bicontinuous structure.Secondary photons thus have secondary paths, exit at secondary pointsand have secondary exit trajectories.

Based upon these dependencies, the entry points and corresponding exitpoints of a particular bicontinuous optical switching structure can beprecisely mapped.

Moreover, since the physical location of the incident beam and the angleof incidence (entrance trajectory) dictate the primary exit point, asingle tunnel can represent multiple entry/exit point pairs. Thus, asingle tunnel can provide a multitude of sub-pathways in either tunnelsystem for multiple beams without the beams impeding each other.

Examples of a single laser beam entering a tunnel at different angles ofentry are illustrated in FIGS. 3 through 6.

As illustrated in FIG. 3, a laser 100 enters a tunnel of thebicontinuous optical switching structure 200 at a certain angle. Basedupon this angle of entry and the corresponding tunnel, the photons 150exit from the bicontinuous optical switching structure 200 at a certainexit point 250.

As illustrated in FIG. 4, a laser 100 enters the same tunnel of thebicontinuous optical switching structure 200 but a different angle.Based upon this different angle of entry, the photons 150 exits from thebicontinuous optical switching structure 200 at a different exit point250.

As illustrated in FIG. 5, photons 100 enter the same tunnel of thebicontinuous optical switching structure 200 but an angle different fromthe angles of FIGS. 3 and 4. Based upon this different angle of entry,the primary photons 150 exit from the bicontinuous optical switchingstructure 200 at still another different exit point 250.

As illustrated in FIG. 6, a laser 100 enters the same tunnel of thebicontinuous optical switching structure 200 but an angle different fromthe angles of FIGS. 3, 4, and 5. Based upon this different angle ofentry, the primary photons 150 exit from the bicontinuous opticalswitching structure 200 at still another different exit point 250.

As previously stated, by directing the laser at different angles ofentry, a mapping of the exit points to entry points can be generated soas to provide an effective switching device.

Examples of multiple laser beams entering a tunnel at different anglesof entry are illustrated in FIGS. 7 through 9.

As illustrated in FIG. 7, multiple laser beams 1000 enter the sametunnel of the bicontinuous optical switching structure 200, but each ata different point on the surface. Based upon these different points ofentry, the primary photons (1510, 1520, 1530, 1540, and 1550) exit fromthe bicontinuous optical switching structure 200 at different points andtrajectories (2510, 2520, 2530, 2540, and 2550), respectively.

As illustrated in FIG. 8, multiple laser beams 1000 enter the sametunnel of the bicontinuous optical switching structure 200, but each ata different point and different from the angles illustrated in FIG. 7.Based upon these different angles of entry, the primary photons (1510,1520, 1530, 1540, and 1550) exit from the bicontinuous optical switchingstructure 200 at different points (2510, 2520, 2530, 2540, and 2550) andtrajectories, respectively.

As illustrated in FIG. 9, multiple laser beams 1000 enter the sametunnel of the bicontinuous optical switching structure 200, but each ata different angle and different from the angles illustrated in FIGS. 7and 8. Based upon these different angles of entry, the primary photons(1510, 1520, 1530, 1540, and 1550) exit from the bicontinuous opticalswitching structure 200 at different points (2510, 2520, 2530, 2540, and2550) and trajectories, respectively.

It is noted that although the Figures show the laser entering one sideof the bicontinuous optical switching structure 200, the laser can enterany tunnel around the bicontinuous optical switching structure 200. Inall the various possibilities of entry points, the exit point of theprimary photons is dictated by the entry point and angle of entry andcan be readily measured and mapped.

The bicontinuous optical switching structure allows each tunnel to havea large number of sub-pathways.

It is noted that the entry point and angle of entry can be controlled bya MEMS mirror system or an optical deflection device. Moreover, theentry point and angle of entry can be set by the positioning of thelaser source or fiber optic or light channel carrying the light beam.

It is further noted that the angular pathways within the tunnel(s)create a form of switching identification (entry/exit point pair) thatis incremental to the information within the beam.

Moreover, a second bicontinuous optical switching structure can be added(stacked) to the first bicontinuous optical switching structure, bymating the tunnel entrance (exit) of one bicontinuous optical switchingstructure to the tunnel exit (entrance) of the other bicontinuousoptical switching structure, to increase selectivity.

Control of the beams and their respective angle of entry can be realizedby deflecting the laser beam from its source to the entrance to thetunnel. There are many forms of modulation of lasers, such as a MEMSmirror system wherein the mirrors can be manipulated to be ON/OFF orhave a particular angle of deflection.

The entry point of a laser beam can be mapped to its measured exit point(of its primary photons) such that the bicontinuous optical switchingstructure can be used to route the laser beam to another switch, to acable, a fiber optic, to an optical storage device, a signal modulator,and/or other optical components.

In addition to deflection, modulation of the beam and/or color can beused to modify the incoming beam for mapping to an output primary photonbeam. Moreover, using interference patterns and/or other forms ofadaptation to the beams to mix with parts of the beam can be utilized inproviding identification for mapping purposes.

As FIGS. 3-9 illustrate, the beam selectivity is largest when the beamhits certain critical points on the surface at certain angles such thata small shift in the angle results in a large change in output path. Amultitude of these critical points exists on the surface of thehyperbolic bicontinuous structures, depending on the intrinsic surfacecurvature of the hyperbolic bicontinuous structures and orientation ofthe hyperbolic bicontinuous structures to the beam. If the beam hitsseveral of these critical points consecutively, the number of possibleoutputs exponentially rises.

Based upon the characteristics of these critical points, a beam can beaimed close to, but not quite exactly on the critical point, to effectvery quick switching, thereby increasing the range of possible pathsthrough the hyperbolic bicontinuous structures. This allows the opticalswitch to effectively operate at the edge of chaos.

Regarding the entry angles of the light entering the optical switch,there are basically three situations involving directing the initiallight source and keeping the mirror fixed: (1) when the light source isoutside the bounding volume of the surface; (2) when the light sourcecomes from within the free space of the bounded surface and (3) when thelight source is embedded in the surface.

For these situations, mirrors (planar or curved) may be used to changethe incident angle relative to the bicontinuous mirror. This would onlyrequire extremely small motions to change the incoming direction of thelight (flexible or not). Moreover, lenses, prisms, gratings, beamsplitters, waveguides, tunable non-linear optical devices, or responsiveoptical elements that change shape/orientation, etc. may be used toachieve different incident angles.

For example, a non-linear waveguide that uses light from a differentsignal to change its optical properties, e.g., refractive index can beused. In this example, a pulsed control laser incident on a non-linearcrystal, wherein the optical properties vary with the frequency of thepulse. In addition, a second laser containing information to be switchedbetween two channels by changing its angle of incidence relative to thebicontinuous mirror is added. If the information is coded at a certainfrequency, the control beam could change the way the waveguide directsthe information and can then act as an optical switch. This could beamplitude gated or other variations.

As illustrated in FIG. 10, a laser source 5000 provides a single laserwhich can be deflected (directed) in multiple directions, as illustratedby the dashed line arrow 5500. The laser 5500 is inputted into abicontinuous optical switching structure 7000, at a predetermined pointof entry or angle.

Within the bicontinuous optical switching structure 7000, activeelectronic circuits, such as laser diodes may be embedded on thehyperbolic surface of the bicontinuous structure such that when thelaser 5500 hits the embedded laser diode, the laser diode is activated.Thus, the single laser 5500 can produce output signals 6000.

The exiting lasers 6000 can be collected by a device 800 for sensing,further transmission, processing, and/or modulation, etc.

FIG. 11 illustrates possible angles of entry for a laser beam (1610,1620, 1630, 1640, and 1650) at an entry point 1700. As illustrated inFIG. 11, the Figure shows the X-Y plane looking down upon the face of atunnel opening in a bicontinuous structure.

It is noted that, in this example, potential laser beams 1620 and 1630follow the same X-Y projection but start from different elevation in theZ direction. In other words, the starting point for laser beam 1620 is(X,Y,Z₁) XYZ space, whereas the starting point for laser beam 1630 is(X,Y,Z₂) in XYZ space.

FIG. 12 illustrates possible angles of entry for a laser beam (1610,1620, 1630, 1640, and 1650) at an entry point 1700. As illustrated inFIG. 12, the Figure shows the X-Z plane across the face of a tunnelopening in a bicontinuous structure.

It is noted that, in this example, potential laser beams 1620 and 1630lie in the same X-Y plane but start from different points in the Zdirection.

It is noted that the hyperbolic bicontinuous structures within theswitching device may be coated electro-optic coatings; such as Braggmirrors that contain periodically spaced layers of non-linear opticalmaterials; that change reflective properties in response to certainlight characteristics.

It is further noted that the electro-optic coatings may be elements thatinteract with photons, such as a lens, diffraction grating, prisms,mirrors, lasers, photodiode, photovoltaic cell, etc.

It is also noted that the incident light may be photons in the visiblespectrum or UV or IR parts of the electromagnetic spectrum.

As noted above, the predictability of entry and exit beam pairs isdependent on the pathway through the hyperbolic bicontinuous structuresand this pathway may be changed by local or global induced distortionsof the pathway, for example using heating or other methods.

FIG. 13 illustrates an example of a device having a hyperbolicbicontinuous structure forming mutually interpenetrating labyrinths.

FIG. 14 illustrates another example of a device having a hyperbolicbicontinuous structure forming mutually interpenetrating labyrinths.

FIG. 15 illustrates a third example of a device having a randombicontinuous structure forming mutually interpenetrating labyrinths.

It is noted that the bicontinuous or polycontinuous structures andvariations thereof may have one set of tunnels closed in order toeliminate any edges. Examples of such structures are illustrated inFIGS. 16 and 17.

FIG. 16 illustrates a D-surface cubosome closed by a sphere.

FIG. 17 illustrates a D-surface cubosome closed by a cube.

FIG. 18 illustrates an annotated example of a device having a hyperbolicbicontinuous structure forming mutually interpenetrating labyrinths. Asillustrated in FIG. 18, the device forms a virtual volume 400 withbounding surface 450. In this example, the device forms a cubic orrectangular volume; however, various other polygonal, irregular, orother volumes could be realized, with their corresponding boundingsurfaces.

In FIG. 18, the device includes one surface comprised of hyperbolicpatches which make up the bicontinuous structure.

It is noted that the opening and exit of the tunnels to the outsidebounding surface of the structure can be flared out, or otherwisedistorted or arranged to enable more or less funneling of light in orout. These flare structures can be seamlessly fused to the tunnelsystem.

It is further noted that the hyperbolic bicontinuous structuresdescribed above may be utilized in various other applications.

For example, the saddle-shaped hyperbolic patches comprising thebicontinuous structures may be used as substrates for creating curvedelectronic devices such as, but not limited to gates, transistors, up tochips and systems on chips

A three-dimensional electronic chip or system can allow for bettercircuitry integration and essentially saves space by containing avertical component relative to a flat substrate, while remaining acontinuous surface on which traces and nodes may be made into one ormore surface-bound circuits

The hyperbolic surface patches comprising the bicontinuous structuresdescribed above allow an extrinsic third dimension without losing theexisting two-dimensionality of conventional chips or systems. Thismaintains an intrinsic physical dimensionality of two whileextrinsically occupying three dimensions.

For example, gates, transistors, memristors, photonic or spintroincdevices, neurons and other biological cells, flat or curved mirrors,LED's, light detectors, antennae, integrated circuits, processors andother circuitry components can be placed on or in the disclosedhyperbolic surface at surface nodes, which are connected by traces,wires or waveguides embedded on or in the surface to other parts of thesurface, or connected by light beams or other EM signals jumping fromone part of the surface to another, to create a three-dimensionalhyperbolic chip or system.

In the described and illustrated hyperbolic bicontinuous structures, onthe surfaces, any point on the surface can be reached by any other pointon the surface without leaving the said surface. This allows the circuitto have an extrinsic three-dimensional structure, while only requiringan intrinsically two-dimensional wiring architecture.

It is noted that two-dimensional wiring indicates that the wiring doesnot leave the surface of the hyperbolic bicontinuous structure. Inconventional three dimensional circuit structures, the wiring musttravel through the substrate structure to connect to circuits at adifferent level.

Examples of a circuit having an extrinsically three-dimensionalstructure, while only requiring an intrinsically two-dimensional wiringarchitecture, are Illustrated in FIGS. 19-24. If desired, wires ortraces (or other information carrying pathways) could be made to leavethe surface of the bicontinuous structure converting the intrinsicallytwo-dimensional wiring architecture into an intrinsicallythree-dimensional architecture.

In FIGS. 19 and 21, the Figures show the wiring and circuit nodes withrespect to their respective hyperbolic surface structures. In FIGS. 20and 22, the Figures show the wiring and circuit nodes with theunderlying hyperbolic surface structure removed. The surface is removedin these figures for clarity to show the embedded network, but couldalso be designed to be removed in applications if so desired, forexample if the surface was selectively dissolved by a substance thatdoes not dissolve the circuit elements.

As illustrated in FIG. 19, a hyperbolic bicontinuous structurecomprising hyperbolic surface patches 1800 has formed thereon wiring ortraces 1850 and circuit nodes 1900. The wiring or traces 1850 areintrinsically two-dimensional in that the wiring or traces 1850 lie inor on the hyperbolic surface 1800, but the wiring or traces 1850 caneffectively travel three-dimensionally between circuit nodes 1900. Thisis realized by the extrinsic three dimensionality of the hyperbolicbicontinuous surface 1800.

FIG. 21 illustrates another example, wherein a hyperbolic bicontinuousstructure, comprising hyperbolic surfaces patches 1800, has formedthereon wiring or traces 1850 and circuit nodes 1900. The wiring ortraces 1850 are two-dimensional in that the wiring or traces 1850 lie inor on the hyperbolic surface 1800, but the wiring or traces 1850 caneffectively travel three-dimensionally between circuit nodes 1900. Thisis realized by the extrinsic three dimensionality of the hyperbolicbicontinuous surface 1800.

FIG. 20 illustrates the circuit architecture with the hyperbolicbicontinuous surface removed. As illustrated in FIG. 20, although thewiring or traces 1850 are two-dimensional with respect to the surface(intrinsic), the wiring or traces 1850 can effectively bethree-dimensional between circuit nodes 1900.

FIG. 22 illustrates another example, wherein the circuit architecture isshown without the hyperbolic bicontinuous surface. As illustrated inFIG. 22, although the wiring or traces 1850 are two-dimensional withrespect to the surface, the wiring or traces 1850 can effectively bethree-dimensional between circuit nodes 1900.

FIG. 23 shows discrete photonic “dots” 1950 that could be embedded on orin the hyperbolic surfaces.

FIG. 24 illustrates an example of a hyperbolic bicontinuous structurewith an embedded projection of an intrinsically two-dimensionalelectronic device 1800.

FIG. 25 illustrates an example of one eight of a unit cell of the“Batwing’ minimal surface structure.

FIG. 26 illustrates an example of a CLP minimal surface structure.

FIG. 27 illustrates another example of a CLP minimal surface structure.

FIG. 28 illustrates an example of a catenoid minimal surface structure.Catenoids can be used to join two otherwise flat parallel surfaces sothat the wiring on one flat surface can be continuous with the wiring onthe second flat, parallel surface.

FIG. 30 illustrates an example of locating circuitry on a hyperbolicbicontinuous structure. As illustrated in the example of FIG. 30, ahyperbolic bicontinuous structure has two sides 1810 and 1820 of thesame structure.

On one side of the hyperbolic surface 1810, circuits 1850 are formed,and on the other side of the hyperbolic surface 1820, circuits 1870 areformed. For most instances, circuits 1850 are electrically isolated fromcircuits 1870. However, the circuits could be connected by signals thatgo through the hyperbolic surface, e.g., via punctures in the surfaceand/or by signals that are propagated through the surface via wires orEM radiation or other means.

FIG. 31 illustrates an example of locating circuitry 1850 on one side ofa hyperbolic bicontinuous structure 1810 and having a coolant 1830 flowalong the other side of the hyperbolic bicontinuous structure 1820.

As illustrated in the example of FIG. 31, a hyperbolic bicontinuousstructure has two sides 1810 and 1820. These surfaces are two sides ofthe same structure.

On one side of the hyperbolic surface 1810, circuits 1850 are formed;however, on the other side of the hyperbolic surface 1820, no circuitsare formed. For this instance, the volume (channel or tunnel system orlabyrinth) bounded by one side of the hyperbolic surface 1820 is usedfor cooling purposes. For example, a coolant fluid could pass throughthe volume, effectively cooling circuits 1850 formed on hyperbolicsurface 1810.

It is noted that the coolant side of the hyperbolic surface 1820 mayalso include various circuitry and devices as on the other side.

Two-dimensional hyperbolic surfaces can enable higher information andswitching density than is possible on a two-dimensional flat chipbecause the surface area spanned at constant radius from a point islarger on the hyperbolic surface than on a flat surface.

Furthermore, circuits built on the bicontinuous surfaces comprisinghyperbolic surface patches may be massively parallel, since the numberof certain non-connected branching circuits that can be built on, forexample, the hyperbolic plane is theoretically infinite. With respect toflat chips, the number of possible parallel, branched, and otherwiseunconnected circuits is zero due to overlaps. This distinction betweenparallel circuits on hyperbolic versus flat Euclidean surfaces arisesout of the falseness of the parallel postulate applied to hyperbolicsurfaces as well known to those skilled in the art of non-Euclideangeometry.

It is further noted that the range of possible physical topologies forconventional flat-substrate-bound circuits is less than the possiblerange for circuits on bicontinuous hyperbolic surfaces.

On the other hand, the hyperbolic bicontinuous structures describedabove can be utilized to physically place the circuit nodes (logicgates, etc.) on a hyperbolic surface rather than on a flat surface.

The hyperbolic bicontinuous structures physically differ from currentsubstrate-based chip designs in allowing extrinsic 3D connectivity yetbeing constructed on a single surface.

In summary, extrinsically three-dimensional devices can be constructedon intrinsically two dimensional structures when those structurescomprise hyperbolic surface patches that are intrinsically twodimensional.

FIG. 23 shows an example of discrete photonic dots that could beembedded on or in a minimal surface device that could be locally flat orhyperbolic. In this example, the photonic dots comprise photoniccrystals joined in different orientations, and form faceted faces likein the cuts of precious gems. The use of faceted photonic dots in aphotonic circuit is enabled by manipulating crystal face junctions toachieve certain effects necessary for optical switching. The alternativeto discrete dots is photonic dots made from cavities in a surface boundphotonic crystal or crystals.

A photonic dot is defined as a photonic crystal that is reduced in sizeto the point where surface modes of the crystal interact with the lightto give non-linear effects. The use of a photonic dot in opticalswitches enables the design of bistable and tristable optical circuits.The non-linearity of the light interacting with the photonic dots allowsan all-optical switch because light can change the effective refractiveindex when incident on an array of photonic dots.

It is noted that a second light path could then be influenced by thefirst due to a switch in the photonic surface resonance. Dyes and othersurface molecules or other matter could help in the control of thenon-linear optical circuitry. Based upon this design, AND, NAND, OR, andNOR gates can be constructed using photonic dots.

In other words, utilization of the photonic dot circuits on thedescribed hyperbolic surfaces a photonic dot circuit based opticalcomputer can be constructed.

Furthermore, since the hyperbolic bicontinuous structures describedabove have near constant curvature, homogeneous distribution networkscan be easily constructed in contrast to the conventionalthree-dimensional Cartesian grids.

The hyperbolic bicontinuous structures described above also provide aphysical geometry for neural net architecture, thereby enablinginterfacing live cultured neurons on the hyperbolic surfaces.

Predictability and tunability are intrinsic in the photonic dots on thehyperbolic bicontinuous structures because of the symmetries in thesephotonic devices. Thus, photonic dots can be combined with dielectricmirrors, aspherical dielectric Fresnel lenses and other opticalcomponents enabling various optical circuits.

These mirrors can be a priori designed to lie on fully predictablenetworked or fully parallel network topologies. Any one surface of thehyperbolic bicontinuous structure may have a very large number of fullyinterpenetrating, yet separate graphs or tree networks, producing highlysymmetric optical network configurations in various classes of tilingsand networks known to those skilled in the art of hyperbolic tilings andnetworks.

The tilings can be seen as the choices of hardware building tiles andthe networks as the circuit elements drawn on the tiles. The nodes aresites where photonic devices can sit and direct the flow of opticalinformation by changing state using other optical circuitry.

In these optical circuits, the number of network topology choices ishigh because of the vast number of possible networks between nodes onthe surfaces. Switching just a few dozen nodes in the possible networkson these surfaces gives high-density information entropy for fullyutilizing the speed of optical circuits.

An example of a simple photonic switch is to use fast photochromics andmodulated pulsed lasers. In this example, the header pulse may be longor short (to turn the transmission ON or OFF) and then the subsequenthigher frequency pulses are allowed to pass the photochromic film ornot. This circuit allows fast optical reactions, color change, beaminterference, and optical computing.

It is further noted that the hyperbolic bicontinuous structures may beutilized in optical environments, electrical environments and/orelectro-optical environments.

The hyperbolic bicontinuous structures provide a two-dimensional designwith the properties to host three-dimensional circuits and networkscomprised of nodes and traces. Within their boundary these surfaces canhave close to constant curvature without sharp edges, can have arelatively large surface area per unit footprint, and/or can enable alarge intrinsic information density flow rate compared to 2D circuitsconfined to flat Euclidean planes.

It is also noted that, as an alternative, the hyperbolic bicontinuousstructures may be filled on one side of the surface to form a poroussolid support for circuitry etc.

It is also noted that bicontinuous surfaces can host circuits of variousmaterials such as topological insulators.

The hyperbolic bicontinuous surfaces may act as substrates for circuitscomprising memristor arrays, thereby enabling a superior performance insolving the von Neumann bottleneck, a problem known to those skilled inthe art of computer architecture, relative to memristor arrays onEuclidean planar surfaces.

Memristors are resistors that remember the amount of current that haspassed therethrough. Memristors can be used as switches and are passivedevices so memristors do not lose their memory when turned off.

Memristors can be constructed on bicontinuous surfaces usingself-assembly and/or three-dimensional lithography. For example,memristors can be implementable on a 3D printed gyroid (bicontinuoussurface) using self-assembly of DNA, for example, as a template fornanowires.

The memristor works by changing the position of oxygen vacancies in anarray of titania cross-bar latches, which forms a transistor thatremembers its former logical state.

By constructing a memristor on a bicontinuous surface, the memristorrealizes a greater efficiency of construction on a flat surface and cantake advantage of the optimal use of the three-dimensionalinterconnectivity circuits built on bicontinuous surfaces provide.

It is noted that light sensitive analogs of memristors may be imprintedor in some way formed or bound on the surface of a mirror-coatedbicontinuous surface or on an optical, electrical or optoelectronic orother circuit embedded on or in a bicontinuous surface. This is alsoapplicable to meminductors and memcapacitors and to other components,devices, or even cells such as light interrogable or light sensitive orlight emitting cells such as, but not restricted to modified neurons.

It is further noted that the above description has been directed tobicontinuous surfaces. The various descriptions are also applicable tomulticontinuous surfaces.

It is further noted that the above description has been directed tobicontinuous surfaces or arbitrary topology or geometry or periodicity.The various descriptions are also applicable, though not restricted toany combination of low and high genus hyperbolic surfaces with orwithout internal symmetry or symmetries with or without translationalperiodicity in one two or three dimensions.

It is further noted that the bicontinuous surface structures can supportcoolant flow on one side of the bicontinuous surface.

In other words, one side of the bicontinuous surface supports thephysical circuits, while the other side of the bicontinuous surfaceprovides the channel for allowing the flow of coolant, therebyeffectively cooling the circuitry in an isolated manner.

It is noted that the bicontinuous surface structures can be utilized tochannel light so as to form a photonic circuit or circuits.

Thus, it is noted that the bicontinuous surface structures can includegrooves or waveguides of nonlinear optical or magneto-optical materialor magnetic field generating circuitry to channel light along thesurfaces.

In another application of the bicontinuous surface structure, octagonalchips can be implemented on the bicontinuous surfaces.

More specifically, the octagonal chips could be bent into the saddles ofthe bicontinuous surface structure, have their pins and complementaryholes on their sides and then connect the chips by a click method tobuild up the bicontinuous structures.

It is noted that there are a number of geometric variations, for example3-sided, 4-sided, 6-sided, and 7-sided chips.

The distinction between a hyperbolic 8-sided chip and a flat 8-sidedchip is explained by dividing the flat “stop sign,” an 8-sided shape,into 8 triangles that meet in the center. Each central angle is 45°.

Since there are 8 triangles, this adds up to 360°, which is what isexpected if a circle is drawn with its center at the center of the chip.In hyperbolic 8-sided chips, the angle is always greater than 360°,because there is more room. This provides the extra surface areacompared with flat chips.

Anticlastic surface is another name for a hyperbolic surface. However itis defined as hyperbolic everywhere but the edges. The bicontinuoussurfaces are made by continuously assembling anticlastic or hyperbolicpatches to form tunnels. They also differ by having flat points of zerocurvature.

Anticlastic surfaces are used commercially for the tension roofs atairports, sports stadiums (parks), and entertainment venues and asarchitectural focus pieces.

Using anticlastic architectural surfaces, electronic circuits can bebuilt on the hyperbolic patches and then the small portions can beassembled into larger pieces.

It is noted that bicontinuous refers to the local condition where thesurface separates two labyrinthine sets of tunnels. However, it is notvalid at the edges of the structure, since the surface terminates andcan therefore not separate anything.

It is further noted that for three-dimensional chips, it is notnecessary to have a completely hyperbolic surface, as it may, in somecases, be sufficient to have a set of two-dimensional stacked chipsjoined by a surface that is locally hyperbolic. However, it is notedthat a bicontinuous surface maximizes speed except for the local flatpoints, not just flat surfaces joined by tunnels.

It is noted that a flexible anticlastic fabric may be made of a flexiblesolar films with embedded circuitry for architectural purposes, and asolar concentrator may be made from a reflective bicontinuous surfacethat funnels and concentrates light downwards into the structure forfurther use.

It is well known to those skilled in the art that bicontinuous, triplyperiodic minimal surfaces such as the gyroid or Batwing surfaces arecomprised of smaller patches related by crystallographic symmetryoperations. Each of these patches is a small saddle-shaped unit withnegative Gaussian curvature. The curvature is defined for each point onthe surface as follows.

A point on a surface, in two dimensions, has two orthogonal principalcurvatures that define its surface curvature. The principal curvaturesare k₁ and k₂, each of the principal curvatures is the inverse of thecorresponding radius of curvature at that point. The mean (H) and theGaussian (K) curvatures are defined as (k₁+k₂)/2 and k₁.k₂,respectively.

Constant mean curvature surfaces include the sphere, the Euclideanplane, and the hyperbolic plane. Here three distinct classes of Gaussiancurvature are defined for points on surfaces, as is well known to thoseskilled in the art of differential geometry.

The first class is defined for points where the Gaussian curvature ispositive, i.e., when the principal curvatures at a point are in the samedirection (i.e., the principal curvatures multiply to give positiveproducts, and thus K>0). These types of curvatures are typical of pointson the surface of closed spheres and other closed ellipsoids and similarsurfaces.

The second class is defined for points where the Gaussian curvature iszero, i.e., when the principal curvatures multiply to give zero i.e.,when either k₁ or k₂ or both=0, and thus K=0. These types of curvaturesare typical of points on the surface of flat planes, cylinders (tubes)and cones.

The third class is defined for points where the Gaussian curvature isnegative, i.e., when the principal curvatures at a point are in oppositedirections, (i.e., the principal curvatures multiply to give negativeproducts, and thus K<0). These types of curvatures are typical of pointson the surface of saddles or hyperbolic surfaces.

When K<0 and H=0, everywhere or nearly everywhere on a surface, theprincipal curvatures are everywhere equal and opposite and the surfaceis a minimal surface. These surfaces are typical of soap films suspendedin a wire frame and are well known to those skilled in the art. Suchsoap films suspended on a boundary wire frame do so with the minimumsurface area, hence the name minimal surface.

Parallel surfaces are defined as parallel to minimal surfaces as iscustomary to those skilled in the art. Parallel surfaces are formed bytranslating each point normal to the minimal surface by distance t.These surfaces have a larger surface area than their correspondingminimal surface.

It should also be noted that any other surface sharing the sameboundary, but not sharing the same geometric coordinates as the minimalsurface will also have a greater surface area than the minimal surfacespanning the same boundary.

By the definition of a minimal surface, any saddle shaped minimalsurface patch containing an embedded network comprised of nodes(devices) and wires/waveguides will have a smaller surface area than anyof its corresponding parallel surfaces or any other surface that spansthe same boundary.

If the embedded nodes and wires/waveguides terminate at the boundary ofthe surface patch (so as to provide continuous hookups when the surfacesare joined), the wire length on the surface patch will also be minimizedon the minimal surface relative to the same network embedded on or inits corresponding parallel surfaces or any other surface that spans thesame boundary.

Since the integrated wire lengths used in a device are an importantfactor in governing the speed of the device, then minimizing these wirelengths is a distinct advantage. Under the condition that these surfacepatches can be formed into a bicontinuous triply periodic minimalsurface by crystallographic symmetry operations, the bicontinuousminimal surface represents a surprisingly efficient structure forperforming very fast 3D computing when the device is fully substratebound.

On a sphere, a geodesic looks like the curved longitude “lines” orflight paths often taken by intercontinental airlines. On a hyperbolicsurface patch, geodesics are also shortest paths between two pointsalong the surface and also appear curved in many situations, thoughsometimes these can be straight lines (in the Euclidean sense).

The above described hyperbolic bicontinuous structures provide a highdegree of predictability about a myriad of different high symmetrycircuits that form short path circuit templates that connect inthree-dimensional space, but are addressable by only two surfacecoordinates (i.e. u, v) rather than the normal Euclidean space (x, y andz).

It is also noted that different modes of the circuitry can be used forcomputing.

For example, a circuit can be constructed by connecting sets of nodes bywires or waveguides embedded on or in the hyperbolic bicontinuoussurface in a manner useful for various operations including but notlimited to storage and retrieval, computation, switching anddistribution.

Components or sub circuitry can be located at nodes so that a partial orcomplete circuit or device can be made on or in a single minimal surfacepatch of limited areal extent. Complete circuits or devices can alsocomprise multiple surface patches decorated with similar or distinctcircuits or devices and joined together at the boundaries of thepatches. Such devices can have node separations that take advantage ofthe scale of the curvature.

With internode distances much smaller than the curvature of thehyperbolic bicontinuous surface, the embedded circuitry and/or devicescan locally very closely resemble conventional, flat (Euclidean)circuits or devices that can be manufactured by conventional means.These relatively flat sub-circuits patches, however, can beinterconnected at a length scale that is of the same order of thecurvature, and therefore, these circuits can be relatively curved andthe circuit becomes extrinsically three-dimensional when extended alongthe surface by repeating the pattern, or partially repeating thepattern.

So the scale of circuitry or sub-circuitry to the scale of the curvatureneeds to be considered when designing the circuitry; however, curvaturevariations on the surface are not critical for small patches where theinternode distance is relatively small.

It is desirable that the curvature variations should be minimized formaximum reduction in integrated wire length, and maximisation of speedin such a device, particularly when the length scales are similar. Themost homogeneous surface, in the sense of homogeneity of curvaturevariation, is Schoen's gyroid (G) surface.

Thus, without being held to theory and for substrate bound circuits anddevices that fill a volume on a single surface, those embedded in or onthe gyroid minimal surface are likely the most for information fortransfer density and speed, when the considerations of relative scaleare taken into account.

Nonetheless, other minimal surfaces known to those skilled in the artmaybe similarly efficient at minimizing wire length. Such surfacesinclude but are not limited to the bicontinuous P-surface, theD-surface, the Batwing surface and many others known to those skilled inthe art.

Lastly, various antenna constructions can be organized to conform tovarious optimization needs. The hyperbolic bicontinuous surfaces mayhave various embedded circuits, labile or not, for a desired antenna orchoice of antennae. These antenna(e) circuits may be responsive toapplied signals.

More specifically, a signal may be transmitted to a bicontinuous surfacecontaining various desired circuits and devices including labilecircuits such that the signal induces, via logical gates andsub-circuitry, a physical change in the antennae configuration as a wayof tuning the antennae for receiving a multiplicity of possible signals.

This could be manifest even within a solid state framework such as acell phone case, or the walls of a truck or spacecraft, etc., configuredfor the type of frequency, signal, distance, etc., of the incomingsignal.

The applied signal may also contain information to cause changes in thesurface reflectivity and/or the shape formation or both of the materialbeing used to control the antenna.

In constructing a three-dimensional circuit on a bicontinuous surfacestructure, graphene ribbons can be utilized.

Graphene ribbons can be cut from larger graphene sheets, or carbonnanotubes can be slit open lengthwise and unfurled or the grapheneribbons could be formed onto pre-existing templates. The grapheneribbons provide a band gap—an energy range that cannot be occupied byelectrons and that determines the physical properties, such as theswitching capability. The width (and edge shape) of the graphene ribbondetermines the size of the band gap, thereby influencing the propertiesof components constructed from the ribbon.

As previously noted, an optical switch may include a plurality ofbicontinuous sub-structures, each bicontinuous sub-structure havingmultiple potential optical entry points and each potential optical entrypoint having a corresponding primary photon exit point, for a giveninput trajectory.

It is defined here that a sub-structural element of a bicontinuoussurface is a small or large fully connected part of a bicontinuoussurface and is here called a bicontinuous sub-structure or surfacepatch.

It is noted that under this definition, the bicontinuous substructure orsurface patch may or may not be bicontinuous.

It is also defined here that a sub-structure of a given bicontinuoussurface can be the given bicontinuous surface itself. This is well knownto those skilled in the art of set theory as the identity set.

It should also be noted that separate bicontinuous structures can beviewed as a union of smaller subsets of a single bicontinuous structure,such that curvature across joined sub-structures can be smooth andcontinuous and without forming holes that could otherwise join the twomutually interpenetrating tunnel labyrinths on either side of thebicontinuous surface.

In this case, the primary or secondary photons exiting one substructurecan act as an input to another substructure. Secondary photons caninclude scattered rather than primary specularly reflected light.

In certain applications, it may useful to define any particular path ofprimary and secondary photons by a nomenclature comprising n symbols,where n=the number of bounces each photon takes transgressing the wholestructure, and whether each successive bounce is along a primary orsecondary path.

For example, a single bounce along the primary path (i.e. a singularspecular reflection event) would be described as a “p” event. Twobounces (n=2) along the primary path would be “pp” or p² events.

If the first bounce sends the photon off the primary path, “s” can beused to describe or name this secondary event.

Thus, exiting photons can have both p and s event history; e.g., p³;p²s.

In some cases, the nomenclature may result in “ . . . sp”, where asecondary photon bounces specularly so that it travels as if it were aprimary photon travelling along a geometrically transformed primarypath.

Thus, a device may have, where the exit photons from a particulartunnel, a combination of pathways involving p and s events, and thesemay arise from paths that have followed separate tunnel branches.

In the case of relatively rough surfaces, the relative ratio of s:pevents will increase relative to that of a perfectly smooth andreflective surface.

It is noted that optical absorption, total internal reflection, Brewsterangle effects and other optical phenomena, not restricted topolarization, interfacial dielectric contrast, emission etc., may leadto a ratio of input photons to emerging photons greater or less thanunity.

It is also noted that exiting photons that follow a path through thebicontinuous structure may have different optical or quantum propertythan when input, for example it may differ in frequency, polarization,state of entanglement etc. compared with its input

Each bicontinuous sub-structure or surface patch may be coated with anelectro-optic or magneto-optic coating or other coating having opticalproperties that change in response to certain light characteristics, forexample its reflection properties.

Furthermore, an optical switch may include a plurality of interconnectedtunnels each delimited by a surface patch, each surface patch havingpredetermined reflective properties, the tunnels forming mutuallyinterpenetrating labyrinths, each tunnel having multiple potentialoptical entry points and each potential optical entry point having acorresponding primary optical exit point for a given input trajectory.

Each tunnel may be coated with an electro-optic coating havingreflective properties that change in response to certain lightcharacteristics. Each surface patch delimiting each tunnel may havepoints that are predominantly hyperbolic.

The plurality of tunnels may be arranged into mutually interpenetratinglabyrinths, divided by a two-sided hyperbolically curved interface. Oneor both tunnel labyrinths on one or both sides of the surface may befilled with an optically transparent or partially transparent material.One tunnel labyrinth on one side of the surface maybe filled with anon-optically transparent material.

In addition, an optical switching system includes a laser light source;an optical switch for receiving a laser light beam from said laser lightsource, said optical switch including a plurality of bicontinuoussub-structures, each bicontinuous sub-structure having multiplepotential optical entry points and each potential optical entry pointhaving a corresponding primary optical exit point for a given inputtrajectory; and a light collection device for receiving photons sourcedfrom the laser light beam after exiting said optical switch. The laserlight source may include a light deflection system for physicallychanging a direction of the laser light beam such that the angle ofincidence of the laser light beam upon the optical switch surface ischanged, thereby changing the optical entry point and trajectory of thelaser light beam.

Each bicontinuous structure or its substructure may be coated on one orboth sides with an electro-optic coating having reflective propertiesthat change in response to certain light characteristics. Eachbicontinuous structure or its substructure may be comprised ofhyperbolic surface patches. The bicontinuous structures contain ahyperbolically curved interface that defines mutually interpenetratingtunnel labyrinths. The laser light source may comprise multiple primaryphoton input paths relative to the bicontinuous structure. Each path mayhave a distinct optical entry point with respect to said optical switchand/or a distinct primary optical exit point with respect to saidoptical switch, for each of the given multiple input trajectories.

A three-dimensional optical switch includes a plurality of bicontinuousstructures. The plurality of bicontinuous structures forms a virtualvolume. Each bicontinuous structure has an opening or openings that aretopologically connected to at least one of the tunnel systems.

The openings are located around a virtual bounding surface of thevirtual volume. Each opening has multiple potential optical entrypoints. Each potential optical entry point has a corresponding primaryoptical exit point for a given input trajectory. Each bicontinuousstructure may be coated with an electro-optic coating having reflectiveproperties that change in response to certain light characteristics.Each bicontinuous structure may comprise hyperbolic surface patches. Thebicontinuous structures may form mutually interpenetrating labyrinthsand contain a hyperbolically curved interface. Each opening may includepotential optical entry points and potential optical exit points.

Furthermore, the bicontinuous surface structures can be embedded withpigments to create various colors or designs. These bicontinuous surfacestructures can be further embedded into fabrics.

The bicontinuous surface circuit containing structures can be packagedfor example by embedding into plastics, polymers or composites toprovide antenna, sensors or computing power or other functionality forelectronic devices.

Moreover, bicontinuous structures can comprise minimal surfaces wherethere are no tight bends along any path on or in the surface (or opticalwaveguides embedded therein) can speed up a signal from point to point,and processing segments can be clustered for optimization along thecontinuum. In such situations, the curving, flowing surfaces can rise upmultiple stories (circuit levels or planes) high and never encounter a90 degree turn.

For example, in the same vertical height as a ten-layer stack, minimaland bicontinuous surface structures can have three times moretransistors and never encounter a 90 degree turn between them. Thisenables the realization of less heat, less power consumption, optimallyshorter paths, and higher connectivity options. The minimal andbicontinuous surface architecture is scalable from connecting logicgates to circuit boards to networked devices.

A three-dimensional circuit includes a plurality of bicontinuous substructures or surface patches; and a plurality of circuit elements. Theplurality of circuit elements are formed, in a two-dimensional manner,on the plurality of bicontinuous sub-structures or surface patches.Bicontinuous structures can be comprised of a plurality of bicontinuoussubstructures or surface patches, where each substructure or surfacepatch can have various sub-circuits of a larger circuit formed from thejoining, fusion, merging or overlapping of substructures or surfacepatches

The bicontinuous sub-structural elements or surface patches may havepoints that have predominantly hyperbolic curvature.

The bicontinuous structures may form mutually interpenetrating tunnellabyrinths and contain a hyperbolically curved interface.

A three-dimensional circuit includes a plurality of tunnels each boundby a surface patch, the tunnels joined, forming mutuallyinterpenetrating tunnel labyrinths; and a plurality of circuit elements.The plurality of circuit elements are formed, in a two-dimensionalmanner, on the plurality of surface patches delimiting their respectivetunnels.

The tunnels may be delimited by surface patches that contain pointshaving predominantly hyperbolic curvature.

The tunnels may form mutually interpenetrating labyrinths divided by ahyperbolically curved interface.

A three-dimensional circuit includes a plurality of bicontinuoussub-structures, the plurality of bicontinuous sub-structures forming avirtual volume, each bicontinuous sub-structure having one or moreopenings; and a plurality of circuit elements. The plurality of circuitelements are formed, in a two-dimensional manner, on the plurality ofbicontinuous sub-structures.

The bicontinuous structure may contain a surface that is predominantlycomprised of points where the surface is hyperbolically curved.

The bicontinuous structures may form mutually interpenetrating tunnellabyrinths and contain a hyperbolically curved interface.

A three-dimensional circuit includes a hyperbolic bicontinuous structureforming a substrate; a first set of nodes formed on one side of thehyperbolic bicontinuous surface; and a first set of electricallyconductive traces formed between the first set of nodes. The first setof electrically conductive traces is formed two-dimensionally on thefirst surface of the hyperbolic bicontinuous structure. The first set ofelectrically conductive traces between the first set of nodeseffectively form a three-dimensional circuit on one side of the surface.

A coolant may be in contact with the second side of a surface defining ahyperbolic bicontinuous structure to provide effective cooling of thefirst set of circuits on the other side.

A second set of circuit nodes may be formed on the other side of thehyperbolic bicontinuous structure, and a second set of electricallyconductive traces may be formed between the second set of circuit nodes.The second set of electrically conductive traces may be formedtwo-dimensionally on the other side of the hyperbolic bicontinuoussurface. The second set of electrically conductive nodes and traces maybe effectively three-dimensional circuits formed on the other side ofthe hyperbolic bicontinuous surface.

The hyperbolic bicontinuous structure may form a plurality of tunnelseach delimited by a surface patch, the tunnels connected formingmutually interpenetrating, but otherwise unconnected labyrinthsdelimited by connected surface patches with no gaps between the patches.

The hyperbolic bicontinuous structure may form a plurality of tunnelseach delimited by a surface patch, the tunnels forming mutuallyinterpenetrating, but otherwise unconnected labyrinths, one of thetunnels labyrinths providing the conduit for the coolant.

An optical switch includes a bicontinuous structure containing aplurality of bicontinuous sub-structures, each bicontinuoussub-structure having multiple potential optical entry points and eachpotential optical entry point having a corresponding primary opticalexit point for a given input trajectory.

Each bicontinuous sub-structure may be coated with an electro-opticcoating.

Each bicontinuous sub-structure may be coated with an electro-opticcoating having reflective properties that change in response to certainlight characteristics.

Each bicontinuous sub-structure may be a hyperbolic surface patch.

The bicontinuous sub-structures may be delimit mutuallyinterpenetrating, but otherwise unconnected tunnel labyrinthspartitioned by a hyperbolically curved interface.

Each potential optical entry point may be a physical location on thebicontinuous structure.

Each potential optical entry point may correspond to a different angleof incidence at a physical location on the bicontinuous structure.

Each potential optical entry point may be a physical location on thebicontinuous structure and wherein each potential optical entry pointcorresponds to a different angle of incidence at a physical location onthe bicontinuous structure such that the multiple potential opticalentry points form a three-dimensional set of potential optical entrypoints.

The bicontinuous structure may be a gyroid minimal surface.

The bicontinuous structure may be the D or diamond minimal surface.

The bicontinuous structure may be the P minimal surface.

An optical switch includes a plurality of tunnels each delimited byhaving a surface patch, each surface patch having predeterminedreflective properties, the tunnels forming mutually interpenetratinglabyrinths, each tunnel representing a set of entry points, each set ofentry points having a multitude of entry angles.

Each tunnel may be coated with an electro-optic coating.

Each tunnel may be coated with an electro-optic coating havingreflective properties that change in response to certain lightcharacteristics.

Each tunnel may be delimited by surface patches whose points havepredominantly hyperbolic curvature.

An optical switching system includes a light source; an optical switchfor receiving a light from the light source, the optical switchincluding a plurality of bicontinuous sub-structures, each bicontinuoussub-structure having multiple potential optical entry points and eachpotential optical entry point having a corresponding optical exit pointfor a given input trajectory; and a light collection device forreceiving light exiting the optical switch sourced from the laser lightbeam.

The light source may be a laser.

The light source may be an LED.

The light source may include a light deflection system for physicallychanging the trajectory or trajectories and entry point or points of theincident light upon the optical switch.

Each bicontinuous sub-structure may be coated with an electro-opticcoating.

Each bicontinuous structure may be coated with an electro-optic coatinghaving reflective properties that change in response to certain lightcharacteristics.

Each bicontinuous sub-structure may be a surface patch with pointspredominantly having hyperbolic curvature.

The bicontinuous structure may form mutually interpenetrating labyrinthswhere the dividing surface is made up of surface patches withpredominantly hyperbolic curvature.

The light source may generate multiple distinct primary light pathsthrough the bicontinuous structure, each path having a distinct primaryoptical entry point with respect to the optical switch.

The light source may generate multiple distinct light paths through thebicontinuous structure, each light path having a distinct primaryoptical exit point with respect to the optical switch.

The light source may generate multiple primary light paths through thebicontinuous structure, each path having a distinct optical entry pointwith respect to the optical switch and a distinct optical exit pointwith respect to the optical switch.

The light source may generate multiple primary and secondary light pathsthrough the bicontinuous structure, each path having a distinct opticalentry point with respect to the optical switch and a distinct opticalexit point with respect to the optical switch.

A three-dimensional optical switch includes a plurality of bicontinuoussub-structures; the plurality of bicontinuous sub-structures forming avirtual volume; each bicontinuous sub-structure having an opening; theopenings being located around a virtual bounding surface of the virtualvolume; each opening having multiple potential optical entry points;each potential optical entry point having a corresponding primaryoptical exit point for a given input trajectory.

Each bicontinuous sub-structure may be coated with an electro-opticcoating.

Each bicontinuous sub-structure may be coated with an electro-opticcoating having reflective properties that change in response to certainlight characteristics.

Each bicontinuous sub-structure may be a surface patch withpredominantly hyperbolic curvature.

The bicontinuous structure may include mutually interpenetrating,otherwise unconnected tunnel labyrinths separated by a hyperbolicallycurved interface.

Each opening may include potential optical entry points and potentialoptical exit points.

A three-dimensional circuit includes a plurality of bicontinuoussub-structures; and a plurality of circuit elements; the plurality ofcircuit elements being formed, in a two-dimensional manner, on theplurality of bicontinuous sub-structures.

Each bicontinuous sub-structure may be a surface patch withpredominantly hyperbolic curvature.

The bicontinuous structures may form mutually interpenetratinglabyrinths and contain a hyperbolically curved interface.

The plurality of circuit elements may include a plurality of neurons.

The plurality of circuit elements may include a plurality of cardiaccells.

The plurality of circuit elements may include a plurality of retinalcells.

The plurality of circuit elements may include a plurality of musclecells.

The plurality of circuit elements may include a plurality of isolatedelectrodes joined by electrically conductive traces each running to thevirtual boundary surface of the bicontinuous structure.

The traces may run along shortest pathways to the boundary.

The shortest pathways may be geodesics of the bicontinuous surface.

A three-dimensional circuit includes a plurality of tunnels eachdelimited by a surface patch, the tunnels forming mutuallyinterpenetrating, but otherwise unconnected tunnel labyrinths; and aplurality of circuit elements; the plurality of circuit elements beingformed, in a two-dimensional manner, on the plurality of surface-patchdelimited tunnels.

Each tunnel may be delimited by surface patches of predominantlyhyperbolic curvature.

The tunnels may form mutually interpenetrating, but otherwiseunconnected labyrinths defining a bicontinuous dividing surfacecontaining surface patches with predominantly hyperbolical curvature.

A three-dimensional circuit includes a plurality of bicontinuoussub-structures, the plurality of bicontinuous sub-structures forming avirtual volume, each bicontinuous sub-structure having an opening; and aplurality of circuit elements; the plurality of circuit elements beingformed, in a two-dimensional manner, on the plurality of bicontinuoussub-structures.

Each bicontinuous sub structure may have a predominantly hyperboliccurvature.

The bicontinuous sub-structures may form mutually interpenetratinglabyrinths and contain a predominantly hyperbolically curved interface.

A three-dimensional circuit includes a hyperbolic bicontinuous structureforming a substrate; a first set of nodes formed on the surface of oneside of the hyperbolic bicontinuous structure; and a first set ofelectrically conductive traces formed between the first set of nodes;the first set of electrically conductive traces being formedtwo-dimensionally on the side of the surface of the hyperbolicbicontinuous structure; the first set of electrically conductive tracesbeing effectively three-dimensional traces between the first set ofnodes.

A coolant may be in contact with the other side of the surface of thehyperbolic bicontinuous structure to provide effective cooling of thefirst set of circuits.

The three-dimensional circuit may further include a second set ofcircuits formed on the other side of the surface of the hyperbolicbicontinuous structure; and a second set of electrically conductivetraces formed between the second set of nodes; the second set ofelectrically conductive traces being formed two-dimensionally on otherside of the surface of the hyperbolic bicontinuous structure; the secondset of electrically conductive traces being effectivelythree-dimensional traces between the second set of nodes.

The hyperbolic bicontinuous structure may include a plurality of tunnelelements having each delimited by a surface patch with predominantlyhyperbolic curvature, the tunnels forming mutually interpenetrating, butotherwise disconnected labyrinths.

The hyperbolic bicontinuous structure may include a plurality of tunnelelements, each delimited by a surface patch with predominantlyhyperbolic curvature, the tunnels forming mutually interpenetrating, butotherwise disconnected labyrinths, one of the tunnel labyrinthsproviding the conduit for the coolant.

While various examples and embodiments have been shown and described, itwill be appreciated by those skilled in the art that the spirit andscope of the embodiments are not limited to the specific description anddrawings herein.

What is claimed is:
 1. An optical switch comprising: a bicontinuousstructure containing a plurality of bicontinuous sub-structures, eachbicontinuous sub-structure having multiple potential optical entrypoints, each potential optical entry point having a correspondingprimary optical exit point for a given input trajectory.
 2. The opticalswitch as claimed in claim 1, wherein each bicontinuous sub-structure iscoated with an electro-optic coating.
 3. The optical switch as claimedin claim 1, wherein each bicontinuous sub-structure is coated with anelectro-optic coating having reflective properties that change inresponse to certain light characteristics.
 4. The optical switch asclaimed in claim 1, wherein each bicontinuous sub-structure is ahyperbolic surface patch.
 5. The optical switch as claimed in claim 1,wherein the bicontinuous sub-structures delimit mutuallyinterpenetrating, but otherwise unconnected tunnel labyrinthspartitioned by a hyperbolically curved interface.
 6. The optical switchas claimed in claim 1, wherein each potential optical entry point is aphysical location on said bicontinuous structure.
 7. The optical switchas claimed in claim 1, wherein each potential optical entry pointcorresponds to a different angle of incidence at a physical location onsaid bicontinuous structure.
 8. The optical switch as claimed in claim1, wherein each potential optical entry point is a physical location onthe bicontinuous structure and wherein each potential optical entrypoint corresponds to a different angle of incidence at a physicallocation on the bicontinuous structure such that the multiple potentialoptical entry points form a three-dimensional set of potential opticalentry points.
 9. The optical switch as claimed in claim 1, wherein thebicontinuous structure is the gyroid minimal surface.
 10. The opticalswitch as claimed in claim 1, wherein the bicontinuous structure is theD or diamond minimal surface.
 11. The optical switch as claimed in claim1, wherein the bicontinuous structure is the P minimal surface.
 12. Anoptical switch comprising a plurality of tunnels each delimited byhaving a surface patch, each surface patch having predeterminedreflective properties, the tunnels forming mutually interpenetratinglabyrinths, each tunnel representing a set of entry points, each set ofentry points having a multitude of entry angles.
 13. The optical switchas claimed in claim 12, wherein each tunnel is coated with anelectro-optic coating.
 14. The optical switch as claimed in claim 12,wherein each tunnel is coated with an electro-optic coating havingreflective properties that change in response to certain lightcharacteristics.
 15. The optical switch as claimed in claim 12, whereineach tunnel is delimited by surface patches whose points havepredominantly hyperbolic curvature.
 16. An optical switching systemcomprising: a light source; an optical switch for receiving a light fromthe light source, said optical switch including a plurality ofbicontinuous sub-structures, each bicontinuous sub-structure havingmultiple potential optical entry points and each potential optical entrypoint having a corresponding optical exit point for a given inputtrajectory; and a light collection device for receiving light exitingsaid optical switch sourced from the laser light beam.
 17. An opticalswitching system as claimed in claim 16, wherein the light source is alaser.
 18. An optical switching system as claimed in claim 16, whereinthe light source is an LED.
 19. The optical switching system as claimedin claim 16, wherein the light source includes a light deflection systemfor physically changing the trajectory or trajectories and entry pointor points of the incident light upon the optical switch.
 20. The opticalswitching system as claimed in claim 16, wherein each bicontinuoussub-structure is coated with an electro-optic coating.
 21. The opticalswitching system as claimed in claim 16, wherein each bicontinuousstructure is coated with an electro-optic coating having reflectiveproperties that change in response to certain light characteristics. 22.The optical switching system as claimed in claim 16, wherein eachbicontinuous sub-structure is a surface patch with points predominantlyhaving hyperbolic curvature.
 23. The optical switching system as claimedin claim 16, wherein said bicontinuous structure forms mutuallyinterpenetrating labyrinths where the dividing surface is made up ofsurface patches with predominantly hyperbolic curvature.
 24. The opticalswitching system as claimed in claim 16, wherein the light sourcegenerates multiple distinct primary light paths through the bicontinuousstructure, each path having a distinct primary optical entry point withrespect to said optical switch.
 25. The optical switching system asclaimed in claim 16, wherein the light source generates multipledistinct light paths through the bicontinuous structure, each light pathhaving a distinct primary optical exit point with respect to saidoptical switch.
 26. The optical switching system as claimed in claim 16,wherein the light source generates multiple primary light paths throughthe bicontinuous structure, each path having a distinct optical entrypoint with respect to said optical switch and a distinct optical exitpoint with respect to said optical switch.
 27. The optical switchingsystem as claimed in claim 16, wherein the light source generatesmultiple primary and secondary light paths through the bicontinuousstructure, each path having a distinct optical entry point with respectto said optical switch and a distinct optical exit point with respect tosaid optical switch.